When line y= x+4 and parabola and the x-axis intersect at point C, find the lengths of the line segments AC and BC

Question

from Kumon level I math page 191b

Answer 1

To find the lengths of line segments AC and BC, we first need to find the coordinates of point C where the line y=x+4 intersects the x-axis.

When y=0, we have:
0 = x+4
x = -4

So, the coordinates of point C are (-4, 0).

To find the lengths of line segments AC and BC, we can use the distance formula:

Length of AC = √((x2-x1)^2 + (y2-y1)^2)
= √((-4-0)^2 + (0-0)^2)
= √(16)
= 4

Length of BC = √((x2-x1)^2 + (y2-y1)^2)
= √((0+4)^2 + (0-0)^2)
= √(16)
= 4

Therefore, the lengths of line segments AC and BC are both 4 units.